Multiscale Dynamics of Bio-Systems: Molecules to Continuum
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Transcript of Multiscale Dynamics of Bio-Systems: Molecules to Continuum
Multiscale Dynamics of Bio-Systems:
Molecules to Continuum
February 2005
Why we need new approaches
• Many degrees of freedom: multidimensional surface, local minima• Interconnected components: strongly or weakly coupled• Hierarchy of scales both in time & space
Bridging regimes: time and length scales from atomistic to continuum
How can we derive lower dimensional models from submicroscopic dynamics that reflect the physico-chemical properties of the system at different scales?
M. Klein
Key question:
How does the molecular fingerprint appearat different time & length scales
Techniques include
• Efficient Numerical Algorithms: Advanced Time-Stepping and Sampling methods
• System Reduction: Algebraic Graph theory, Computational Geometry, Convex Optimisation
• Continuous Representations: Finite volume, Adaptive meshing
Integrated Multidisciplinary Approach
•At the Interface of Science, Engineering, Biology
•From Departments of Aeronautics, Bioengineering, Chemistry, Mathematics…
•M.A. Robb Ab-initio and QM/MM methodology for chemical Reactivity
•I.R. Gould Hybrid QM/MM, Parallel MD, Force-field Development
•S.N Yaliraki Coarse graining with Convex Optimisation
•M. Barahona Graph theory, Nonlinear System Reduction, Dynamical Systems
•K.H. Parker Biomechanics, Physiological Fluid Dynamics, Heamodynamics
•J. Peiro´ Automatic generation of unstructured meshes, Biomedical Fluid Dynamics
A. Efficient Numerical Algorithms for Atomistic Simulations
Advanced time-stepping and sampling methods –SDEs, Symplectic methods
Improved empirical potentials and Quantum/Classical interface Gould, Robb
Identify optimal pathways that connect main structures
Global Optimisation (SOS, SDP) Parrilo, Jadbabaie,Yaliraki
Multiscale approaches in BioMolecular Modelling
Identify Global Conformational motions
Discrete ProbabilityReversible Markov Chains
Deduce state-based graphs
C. Continuous Representations
Finite volume approaches to mesh generation for biomolecules
- Parker, Yaliraki, Peiró
Reduce the multidimensional space
Computational Geometry & Global Optimisation Compatible, geometric-based models that satisfy constraints Yaliraki
Nonlinear System Reduction Barahona, Parrilo
Geometric graphs
Algebraic Graph theory -Barahona, Jadbabaie
Neighborhood graphs
B. System Reduction
A few examples
Self Assembly of Viral Capsids
Barahona et al.
100 nm
Amyloid Fibril Formation in Neurodegenerative Diseases
Yaliraki et al. (e.g., Burke et al, PNAS 100, 2003)
m (length)nm (diameter); hours to ?? (Fig: Soto et al)
Protein-Membrane Interactions: Signalling
Gould et al.nm-m; fs to hours
Cornell et al, J.Am.Chem.Soc. 117 (95)Hughes et al, BMC Structural Biology, 3 (03)
Connective Tissue: Cartilage
Parker et al.
mm; hours
Ehrlich et al, Biorheology 35 (98)Mestel et al, Biorheology 35 (98)
Design of Molecular Circuitry at the Nanoscale
Molecular Electronics
Bio-sensors
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